Evaluate the standard deviation, Applied Statistics

You have an assembly line which produces 1L bottles of seltzer with a standard deviation of 0.05L.

• Assuming the distribution of volume is normal, what is the chance any single bottle's volume is between 0.85L and 0.95L?

• If you chose 100 bottles at random, what would be the expected average volume of the bottles in your sample? What would the standard deviation of the sample average be? What is the shape of this distribution? Give reasons for your answers.

• If you pulled a sample of 50 bottles, what is the chance that you would find the average volume was greater than 0.99L?